Question

Use L'Hopitals Rule to evaluate the following limit.

lim x-> 0 ( sin(8x) - 8x cos(8x) ) / ( 8x - sin(8x) )

Please use L'Hopitals Rule please

Answer #1

Note: to find the limit we use l'hospital rule.

Details explained in the image

Finding Limits: Use L’Hopital’s rule to evaluate the limit .
SHOW WORK .
8. lim┬(x→-1)〖(x-8x^2)/(12x^2+5x)〗
9. lim┬(x→0)〖sin5x/(2x^2 )〗

1. Evaluate the limit using L'Hospital's rule if necessary
lim x→∞ (1+ 12 / x)^x/1
2. In which limits below can we use L'Hospital's Rule?
lim x→π/5 sin(5x) /5x−π
lim x→−∞ e^−x / x
lim x→0 2x/ cotx
lim x→0 sin(3x) / 3x
I Need help with both questions please! thank you so much.

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lim x→0 1−e^x /sin(2x)
lim x→0 x+tanx /sinx
lim x→−∞ e^−x /x

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lim x→0+ (9x)sin(4x)

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1.
Find the area of the shaded region.
2. Find the limit. Use l'Hospital's Rule where appropriate. If
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lim x → 0
1 + 10x
−
1 − 3x
x
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